Furey worked as a teacher for the Roman CatholicSchool Board in St. John's from 1969 to 1972. From 1972 to 1978, he was a Supervising Vice Principal with the Port-au-Port Roman Catholic School Board and from 1978-80 Supervising Principal of the Placentia-St. Mary's Roman Catholic School Board.

On August 11, 1999, Furey was appointed to the Senate on the advice of Prime MinisterJean Chrétien. He sits as a Liberal and serves as Chair of the Standing Committee on Internal Economy, Budgets and Administration.

On January 29, 2014, Liberal Party leader Justin Trudeau announced all Liberal Senators, including Furey, were removed from the Liberal caucus, and would continue sitting as Independents.[1] According to Senate Opposition leader James Cowan, the Senators will still refer to themselves as Liberals even if they are no longer members of the parliamentary Liberal caucus.[2]